In triangle QRS, QR = 8 and RS = 5. Which expresses all possible lengths of side QS?
Answer:
[tex]3<QS<13[/tex]
Step-by-step explanation:
We have been given that in triangle QRS, [tex]QR=8[/tex] and [tex]RS=5[/tex]. We are asked to find the possible lengths of side QS.
We will use triangle inequality theorem to solve for QS.
Triangle inequality theorem states that sum of two sides of triangle must be greater than third side.
[tex]QS+RS>QR[/tex]
[tex]QS+5>8[/tex]
[tex]QS+5-5>8-5[/tex]
[tex]QS>3[/tex]
[tex]QS<RS+QR[/tex]
[tex]QS<5+8[/tex]
[tex]QS<13[/tex]
Upon combining both solutions, we will get:
[tex]3<QS<13[/tex]
Therefore, the solution [tex]3<QS<13[/tex] expresses all possible lengths of side QS.
Answer:
3<QS<13
Step-by-step explanation:
edg 2021
Justin and Pedro each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. Pedro launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Pedro’s rocket?
Answer:
Equation of Pedro's rocket
[tex]h= -16t^2+120t+2[/tex]
Equation of Pedro's rocket [tex]h= -16t^2+120t+2[/tex]
Step-by-step explanation:
[tex]h= -16t^2+60t+2[/tex]
on comparing the given equation with general equation
[tex]h= -gt^2+vt+h_{0}[/tex]
we get v = 60 feet /second which is the speed of Justin's rocket.
Speed of Pedro's rocket = double of Justin's rocket
= 2(60 ) = 120 feet second
therefore equation for Pedro will be given by
[tex]h= -16t^2+120t+2[/tex]
A rocket car on the bonneville salt flats is traveling at a rate of 640 miles per hour. How much time would it take for the car to travel 384 miles at this rate?
Answer:
0.6 hour or 36 minutes
Step-by-step explanation:
We can use proportion to solve this problem.
640 miles = 1 hour
384 miles = x
cross-multiply
640 x = 384
Divide both-side of the equation by 640
[tex]\frac{640x}{640}[/tex] = [tex]\frac{384}{640}[/tex]
(On the left-hand side of the equation 640 at the numerator will cancel-out 640 at the denominator, while on the right-hand side of the equation 384 will be divided by 640)
x = [tex]\frac{384}{640}[/tex]
x = 0.6 hour
or
x = 0.6×60 = 36 minutes
Therefore the time it would take the car to travel 384 miles is 0.6 hour or 36 minutes
There are 7 people at a party. Each person must shake hands with all the other people at the party once. How many handshakes does it take to do this?
Answer:
Step-by-step explanation:
21
20i + 5i=
a.15i
b.25i
c.20i
The equation of line WX is y = −2x − 5. Write an equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2)
y = 1 over 2x + 3 over 2
y = negative 1 over 2x + 3 over 2
y = 1 over 2x − 3 over 2
y = − 1 over 2x − 3 over 2
How do I give a "parametrization for the curve": the ray with initial point (2,5) that passes through (-1,0)? ...?
Find a polynomial function f(n) such that f(1), f(2), ... , f(8) is the following sequence.2, 8, 14, 20, 26, 32, 38, 44
An interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 21 inches on the architect’s plan. What is the actual length of the room in feet if the scale of the plan is 1.75 inches to 1 foot?
Answer:
12 inches i think
Step-by-step explanation:
because 21 ft = 252 ''
1.75* 12 = 21 ft
252/21 = 12ft
but im not 100% sure, I'll let yk once
I find out..
If The length of the room is 21 inches on the architect’s plan the actual length of the room is in feet if the scale of the plan is 1.75 inches to 1 foot is 36.75 feet.
What is the scale factor?It is defined as the multiplication factor used for the design of an object with respect to some other object . the scale is generally used to design prototype designs of large objects. It is also used in interior design planning rooms.
It is multiplied by the design dimension to get the actual size of the object or product.
For the given question an interior designer is planning a room but needs to first figure out the dimensions. The length of the room is 21 inches on the architect’s plan. the scale of the plan is 1.75 inches to 1 foot means the scale factor is 1.75
The actual length of the room = 1.75 ×21
= 36.75 feet
learn more about scale factors from here
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If a polygon has six sides, then it is a hexagon. true or false.
what is the equation in point slope form of a line that passes through the point (–8,2) and has a slope of 1/2?
Which is a table of values for y=x-6? Show all work.
A. X y
-5 1
-8 -14
-7 -13
B. X y
-5 -11
-8 -2
-7 -13
C. X Y
-5 -11
-8 -14
-7 -13
D. X Y
-5 1
-8 -2
-7 -1
what is a expression that represents the sum of 7 and x
An isosceles triangle has an area of 24 cm^2, and the angle between the two equal sides is 5π/6. What is the length of the two equal sides? (Round your answer to one decimal place.)
Final answer:
To find the length of the two equal sides of an isosceles triangle with a given area and angle, we use a formula involving the sides and angle. By substituting the given values and applying trigonometry, we determine the length of the sides is approximately 9.8 cm.
Explanation:
To find the length of the two equal sides of an isosceles triangle with an area of 24 cm² and an angle between these sides of 5π/6, we can use the formula for the area of a triangle, which is A = ½ × base × height. However, in this scenario, it's more relevant to apply the formula involving the sides and the included angle, given by A = ½ × b × c × sin A, where b and c are the lengths of the two equal sides, and A is the included angle.
Substituting the given values, we get 24 = ½ × b² × sin(5π/6). Sin(5π/6) is ½, so we have 24 = ½ × b² × ½. Simplifying, b² = 96, and therefore b ≈ 9.8 cm. Thus, the length of the two equal sides is approximately 9.8 cm, rounded to one decimal place.
What is the average rate of change of the function below on the interval from x = 0 to x = 2?
f(x)=250(0.5)x
Question 8 options:
A.-93.75
B.62.5
C.0
D.-0.25
Which of the following statements is false?
A)The product of two rational numbers is always irrational.
B)The sum of a rational number and an irrational number is always irrational.
C)The product of a nonzero rational number and an irrational number is always irrational.
D)The product of two irrational numbers is either rational or irrational.
Answer:
A.
Step-by-step explanation:
So if you do √25*√49 is 13.2287565553
which is irrational but if you do 53 times 53 you get 2809 which is rational so you its Not always irrational
James deposited $575 into a bank account that earned 5.5% simple interest each year. If no money was deposited into or withdrawn from the account, how much money was in the account after 2 years? Round your answer to the nearest cent. Enter your answer in the box.
Answer:
it's 654.06
Step-by-step explanation:
I just did the test
if y+7=21, what is the value of y?
Ok so if the problem is y+7=21, what the number that multiplies by 7 and you get 21. And your answer should be the answer after you figured out the problem.
You are designing a rectangular poster to contain 50 in^2 of printing with a 4 in. margin at the top and bottom and a 2 inch margin at each side. What overall dimensions will minimize the amount of paper used? ...?
To minimize the amount of paper used for a rectangular poster with 50 square inches of printing area and specified margins, the overall dimensions should be approximately 9.59 inches in width and 16.95 inches in height.
To find the overall dimensions of the rectangular poster that minimize the amount of paper used, let's start by stating the problem mathematically. The poster must contain 50 square inches of printing area. The poster has margins of 4 inches at the top and bottom, and 2 inches on each side.
Let the dimensions of the printing area be width w and height h. Therefore, we know:
w * h = 50 square inches
Including the margins, the overall dimensions of the poster will be:
Overall width = w + 2 + 2 = w + 4Overall height = h + 4 + 4 = h + 8We aim to minimize the total area of the poster including the margins, which is given by:
A = (w + 4)(h + 8)
From the constraint w * h = 50, we can express h in terms of w as follows:
h = 50 / w
Substituting this into the total area formula:
[tex]A(w) = (w + 4)igg(rac{50}{w} + 8igg) = (w + 4)(rac{50}{w} + 8)[/tex]
To minimize A(w), we take the derivative with respect to w and set it to zero. This involves some calculus:
First, expand the equation:A(w) = 50/w + 8w + 200/w + 32Simplify to A(w) = 250/w + 8w + 32Take the derivative dA/dw and set it to zero:
dA/dw = -250/w² + 8 = 0
Solving for w:
-250/w² = -8
w² = 250/8 = 31.25
w = √31.25 ≈ 5.59 inches
Using the constraint w * h = 50:
h = 50/w = 50/5.59 ≈ 8.95 inches
Therefore, the overall dimensions of the poster are:
Width: w + 4 ≈ 5.59 + 4 ≈ 9.59 inchesHeight: h + 8 ≈ 8.95 + 8 ≈ 16.95 inchesThus, to minimize the amount of paper used, the overall dimensions should be approximately 9.59 inches by 16.95 inches.
How do u write "03 December 2015" in 5 letters without using numbers ??
What is 5 medium apples divided by 475 calories?
The table below represents the velocity of a car as a function of time:
Time (hour) x Velocity (miles/hours) y
0 50
1 52
2 54
3 56
Part A: What is the y-intercept of the function, and what does this tell you about the car? (4 points)
Part B: Calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points)
Part C: What would be the domain of the function if the velocity of the car was measured until it reached 60 miles/hour and the car does not change motion? (2 points)
Answer:
Part A: The y-intercept of the function is 50. It means the initial velocity is 50 miles/hours.
Part B: The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.
Part C: If the velocity of the car is 60 miles/hour, then the domain is 5.
Step-by-step explanation:
Part A:
From the given table it is clear that at x=0 the value of y is 50.
It means the y-intercept of the function is 50. It represents that the initial velocity is 50 miles/hours.
Part B:
From the given table it is clear that at x=1 the value of y is 52 and at x=3 the value of y is 56. It means the graph passes through two points (1,52) and (3,56).
The average rate of change of the function is
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{56-52}{3-1}=\frac{4}{2}=2[/tex]
The average rate of change of the function represented by the table between x = 1 to x = 3 hours is 2. It means the velocity increases by 2 miles per hour.
Part C:
The slope intercept of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
The slope of the function is 2 and y-intercept is 50, therefore the equation of function is
[tex]y=2x+50[/tex]
Put y=60 in the above equation, to find the domain at velocity 60 miles/hours.
[tex]60=2x+50[/tex]
Subtract 50 from both the sides.
[tex]60-50=2x[/tex]
[tex]10=2x[/tex]
Divide both sides by 2.
[tex]\frac{10}{2}=x[/tex]
[tex]5=x[/tex]
Therefore the domain is 5 if velocity is 60 miles/hours.
The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.04x2 + 1.56x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the approximate maximum height of the football?
the answer is A. 15.21 yd
P is 9 more than half of q
What is the probability of rolling double six
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
Its drag to files
Answer:
Step-by-step explanation:
Which is the best estimate for 8,104 ÷ 37?
A.
2
B.
20
C.
200
D.
2,000
Explain how to find an unknown value in a ratio by using a unit rate.
We may write ratios as fractions to make it easier to determine the unknown term, and then utilize some fraction sense or cross-multiply to find the answer.
What is the ratio?Two quantities are compared in order to ascertain how frequently one yields the other. A fraction or a sign between two numbers can be used to denote the percentage.
We have to find an unknown value in a ratio by using a unit rate.
By lowering the fraction so that the first term serves as the denominator or the second term, you may express any rate as a unit rate.
To begin with, we must define a ratio, which is the comparison of two measures or values. Simply laying one number over the other, like in division, creates the basic form of a unit rate.
Think of a rate as a specific ratio with words that consists of two separate units or entities. It's like putting the simplest and most practical definition of what something is equivalent.
Thus, it is possible to find an unknown value in a ratio by using a unit rate.
Learn more about the ratio here:
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Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?
x + y < 8
x + y > 8
x + y ≤ 8
x + y ≥ 8
Answer:
The correct answer for E2020 is C: x + y ≤ 8
Hope this helps you
(p.s:Please mark me as brainlyest)
Step-by-step explanation:
I just took the test on edu and got 100%
A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
Answer:
28.47º of latitude, 7.35º of longitude
Step-by-step explanation:
The latitude and longitude are simple imaginary lines (horizontal for latitude and vertical for longitude) that divide the Earth from an angle point of view. When used as a combination of both, you can get an exact location in any part of the world. For the 2 references, there a 0º divisions that make one side positive angles and negative on the other side (in the case of latitude, positive angles are above the equator line and for longitude positive angles are from the right of the Greenwich Meridian).
With the above mentioned we can observe that Hong Kong and Jakarta are away 22.27º and 6.2º respectively from the equator. So, the total degrees in latitude wil simply be the sum of the 2 absolute values (222.7º+6.2º) giving as a result of 28.47º.
On the other hand, we have in longitude that both cities are several degrees away from the same reference, and because they are from the right side of the Greenwich Meridian, the net change will be the substraction of 114.5-106.8º, giving as a result a total of 7.35º.